The present invention relates generally to sigma delta modulators. More specifically, a sigma delta modulator with noise shaping is disclosed.
Analog to digital converters (ADCs) are widely used in electronic systems for digitizing signals. The conversion from analog signal to digital introduces noise into a system, referred to as quantization noise resulting from the quantization process. FIG. 1A shows the noise transfer function (NTF) of a Nyquist ADC. A Nyquist ADC is one type of ADC that samples the input signal at twice the bandwidth, which is a sampling rate adequate for recovering the original signal according to the Nyquist theorem. The NTF of the Nyquist SDM tends to be relatively flat, and does not reduce the noise.
Attempts have been made to ameliorate the noise problem using oversampled ADCs, also known as sigma delta modulators (SDMs), to provide noise shaping. FIG. 1B illustrates the noise transfer function of a sigma delta modulator. The input signal is sampled at a rate greater than twice the bandwidth. The NTF of the SDM has a minimum centered at direct current (DC) that forms a notch in the signal spectrum. The presence of this notch in the NTF provides noise shaping. Thus, the output noise is reduced at frequencies around the notch.
The benefits of an oversampled SDM generally come from the use of a large oversampling ratio. As the oversampling ratio decreases, the dynamic range of the SDM decreases. To meet certain dynamic range requirements, some designs use multiple cascaded stages to achieve a lower oversampling ratio. FIG. 1C illustrates the noise transfer function of a cascaded sigma delta modulator. With multiple cascaded stages, the notch in the NTF deepens at DC, and provides further noise reduction at frequencies around DC. However, the improvement in noise reduction due to each stage diminishes as more stages are cascaded.
For sigma delta modulators used in wide band applications such as wireless local area network devices, it is desirable to reduce noise for a broader frequency range. In xe2x80x9cA TWO-PATH BANDPASS SIGMA-DELTA MODULATOR WITH EXTENDED NOISE SHAPINGxe2x80x9d by Tabatabaei, et al. (IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 35, NO. 12, DECEMBER 2000) which is incorporated by reference, Tabatabaei discloses a way to produce minima in the NTF at frequencies other than DC, by digitally mixing the output of one stage with another frequency. FIG. 1D illustrates the noise transfer function of a two stage sigma delta modulator that uses digital mixing, according to Tabatabaei. The cascaded stage produces a minimum in its transfer function that is offset from DC. As a result, in the NTF, there is an additional notch centered at f0 besides the one at DC. The NTF is shaped to reduce noise near both notches. This design is superior to the conventional cascaded SDM in terms of noise characteristics, but a number of problems remain. The digital mixer adds complexity to the circuitry and consumes more power. The mixer frequency is dependent on the system clock and may only take on a limited number of values. Also, the mixer is designed to output a single frequency, therefore the location of the additional minimum cannot be easily moved.
It is desirable to have a wide band SDM that has broader noise reduction without increasing circuitry complexity and power consumption. It would also be useful to control the location of the minimum in the NTF more easily.